Question 1153626: 6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
a. Use the five steps of hypothesis testing.
b. Figure the confidence limits for the 95% confidence interval.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! I need the standard deviation of the 20 scores unless I can assume it was 10.
Ho: means were the same
Ha: they weren't
alpha=0.05, P{reject Ho|Ho true}
critical value |z|>1.96
calculation z=(78-75)/10/sqrt(20)
=3*sqrt(20)/10=1.34
Fail to reject Ho; insufficient evidence to say the scores were >75.
CI half-interval is +/-1.96 *10/sqrt(20) and that is added or subtracted to the mean.
this is 4.38 or 4.4
CI is (73.6, 82.4)
Since 75 is in the CI, this is consistent with failure to reject.
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